Decorrelation-Based Feature Discovery: Activity-Whole
Jose Tamez
2023-10-06
- 1 Effect of UPLTM-Based Decorrelation
on Feature Discovery
- 1.0.1 Loading the libraries
- 1.1 Material and Methods
- 1.2 The Data
- 1.3 Generaring the report
- 1.4 The heatmap of the data
- 1.5 The decorrelation
- 1.6 The heatmap of the decorrelated data
- 1.7 The correlation matrix after decorrelation
- 1.8 U-MAP Visualization of features
- 1.9 Univariate Analysis
- 1.10 Comparing ILAA vs PCA vs EFA
- 1.11 Effect on CAR modeling
1 Effect of UPLTM-Based Decorrelation on Feature Discovery
1.0.1 Loading the libraries
library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)
op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)1.1 Material and Methods
Data Source https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6960825/
Mohino-Herranz I, Gil-Pita R, Rosa-Zurera M, Seoane F. Activity Recognition Using Wearable Physiological Measurements: Selection of Features from a Comprehensive Literature Study. Sensors (Basel). 2019 Dec 13;19(24):0. doi: 10.3390/s19245524. PMID: 31847261; PMCID: PMC6960825.
1.2 The Data
Activitydata <- read.csv("~/GitHub/LatentBiomarkers/Data/ActivityData/data.txt", header=FALSE, stringsAsFactors=TRUE)
featNames <- read.table("~/GitHub/LatentBiomarkers/Data/ActivityData/Featurelabels.txt", quote="\"", comment.char="")
featNames <- as.character(t(featNames))
featNames <- str_replace_all(featNames,"\\(abs\\)","_A_")
featNames[duplicated(featNames)] <- paste(featNames[duplicated(featNames)],"D",sep="_")
rep_ID <- numeric(nrow(Activitydata))
ctr <- 1
for (ind in c(1:(nrow(Activitydata)-1)))
{
rep_ID[ind] <- ctr
if (Activitydata$V1[ind] != Activitydata$V1[ind+1]) ctr <- 0;
ctr <- ctr + 1
}
rownames(Activitydata) <- paste(Activitydata$V1,rep_ID,sep="_")
colnames(Activitydata) <- c("ID",featNames,"class")
Activitydata$rep <- rep_ID
tb <- table(Activitydata$class)
classes <- c("Neu","Emo","Men","Phy")
names(classes) <- names(tb)
Activitydata$class <- classes[as.character(Activitydata$class)]
table(Activitydata$class)
#>
#> Emo Men Neu Phy
#> 1120 1120 1120 1120
ID_class <- paste(Activitydata$ID,Activitydata$class)
IDCLASS <- unique(ID_class)
theclass <- Activitydata$class[!duplicated(ID_class)]
theIDs <- Activitydata$ID[!duplicated(ID_class)]
ActivitydataAvg <- NULL
for (id in IDCLASS)
{
ActivitydataAvg <- rbind(ActivitydataAvg,apply(Activitydata[ID_class==id,featNames],2,mean))
}
colnames(ActivitydataAvg) <- featNames
rownames(ActivitydataAvg) <- IDCLASS
ActivitydataAvg <- as.data.frame(ActivitydataAvg)
ActivitydataAvg$class <- theclass
ActivitydataAvg$ID <- theIDs
table(ActivitydataAvg$class)
#>
#> Emo Men Neu Phy
#> 40 40 40 40
ActivitydataAvg <- subset(ActivitydataAvg, class=="Men" | class=="Emo")
ActivitydataAvg$class <- 1*(ActivitydataAvg$class == "Men")
table(ActivitydataAvg$class)
#>
#> 0 1
#> 40 401.2.0.1 Standarize the names for the reporting
studyName <- "Activity"
dataframe <- ActivitydataAvg
outcome <- "class"
TopVariables <- 10
thro <- 0.80
cexheat = 0.15
1.3 Generaring the report
1.3.1 Libraries
Some libraries
library(psych)
library(whitening)
library("vioplot")
library("rpart")1.3.2 Data specs
pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))| rows | col |
|---|---|
| 80 | 534 |
pander::pander(table(dataframe[,outcome]))| 0 | 1 |
|---|---|
| 40 | 40 |
varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]
largeSet <- length(varlist) > 1500 1.3.3 Scaling the data
Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns
### Some global cleaning
sdiszero <- apply(dataframe,2,sd) > 1.0e-16
dataframe <- dataframe[,sdiszero]
varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
dataframe <- dataframe[,tokeep]
varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]
iscontinous <- sapply(apply(dataframe,2,unique),length) >= 5 ## Only variables with enough samples
dataframeScaled <- FRESAScale(dataframe,method="OrderLogit")$scaledData1.4 The heatmap of the data
numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000
if (!largeSet)
{
hm <- heatMaps(data=dataframeScaled[1:numsub,],
Outcome=outcome,
Scale=TRUE,
hCluster = "row",
xlab="Feature",
ylab="Sample",
srtCol=45,
srtRow=45,
cexCol=cexheat,
cexRow=cexheat
)
par(op)
}
1.4.0.1 Correlation Matrix of the Data
The heat map of the data
if (!largeSet)
{
par(cex=0.6,cex.main=0.85,cex.axis=0.7)
#cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
cormat <- cor(dataframe[,varlist],method="pearson")
cormat[is.na(cormat)] <- 0
gplots::heatmap.2(abs(cormat),
trace = "none",
# scale = "row",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Original Correlation",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Pearson Correlation|",
xlab="Feature", ylab="Feature")
diag(cormat) <- 0
print(max(abs(cormat)))
}
[1]
1
1.5 The decorrelation
DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#>
#> ECG_PSD_median EDA_Filt1_prctile75_D EDA_Functionals_power_Fil12trimmean25 IT_LF_prctile25 EDA_Functionals_power_Originalskewness_D EDA_Original_kurtosis
#> ECG_original_mean ECG_original_std ECG_original_trimmean25
#> 0.12672176 0.78787879 0.12396694
#> ECG_original_median ECG_original_skewness ECG_original_kurtosis
#> 0.18457300 0.06060606 0.05785124
#>
#> Included: 363 , Uni p: 0.0004132231 , Base Size: 11 , Rcrit: 0.366515
#>
#>
1 <R=1.000,thr=0.950>, Top: 40< 1 >[Fa= 40 ]( 40 , 194 , 0 ),<|><>Tot Used: 234 , Added: 194 , Zero Std: 0 , Max Cor: 1.000
#>
2 <R=1.000,thr=0.950>, Top: 35< 3 >[Fa= 71 ]( 33 , 104 , 40 ),<|><>Tot Used: 262 , Added: 104 , Zero Std: 0 , Max Cor: 1.000
#>
3 <R=1.000,thr=0.950>, Top: 22< 2 >[Fa= 90 ]( 22 , 53 , 71 ),<|><>Tot Used: 277 , Added: 53 , Zero Std: 0 , Max Cor: 1.000
#>
4 <R=1.000,thr=0.950>, Top: 8< 1 >[Fa= 96 ]( 8 , 27 , 90 ),<|><>Tot Used: 277 , Added: 27 , Zero Std: 0 , Max Cor: 1.000
#>
5 <R=1.000,thr=0.950>, Top: 5< 4 >[Fa= 100 ]( 5 , 12 , 96 ),<|><>Tot Used: 277 , Added: 12 , Zero Std: 0 , Max Cor: 1.000
#>
6 <R=1.000,thr=0.950>, Top: 3< 4 >[Fa= 102 ]( 3 , 6 , 100 ),<|><>Tot Used: 277 , Added: 6 , Zero Std: 0 , Max Cor: 1.000
#>
7 <R=1.000,thr=0.950>, Top: 1< 4 >[Fa= 102 ]( 1 , 4 , 102 ),<|><>Tot Used: 277 , Added: 4 , Zero Std: 0 , Max Cor: 1.000
#>
8 <R=1.000,thr=0.950>, Top: 1< 4 >[Fa= 102 ]( 1 , 4 , 102 ),<|><>Tot Used: 277 , Added: 4 , Zero Std: 0 , Max Cor: 1.000
#>
9 <R=1.000,thr=0.950>, Top: 1< 4 >[Fa= 102 ]( 1 , 4 , 102 ),<|><>Tot Used: 277 , Added: 4 , Zero Std: 0 , Max Cor: 1.000
#>
10 <R=1.000,thr=0.950>, Top: 1< 3 >[Fa= 103 ]( 1 , 3 , 102 ),<|><>Tot Used: 277 , Added: 3 , Zero Std: 0 , Max Cor: 0.950
#>
11 <R=0.950,thr=0.900>, Top: 53< 1 >[Fa= 122 ]( 46 , 60 , 103 ),<|><>Tot Used: 296 , Added: 60 , Zero Std: 0 , Max Cor: 1.000
#>
12 <R=1.000,thr=0.950>, Top: 8< 1 >[Fa= 124 ]( 8 , 8 , 122 ),<|><>Tot Used: 296 , Added: 8 , Zero Std: 0 , Max Cor: 0.950
#>
13 <R=0.950,thr=0.900>, Top: 14< 1 >[Fa= 130 ]( 11 , 11 , 124 ),<|><>Tot Used: 301 , Added: 11 , Zero Std: 0 , Max Cor: 0.997
#>
14 <R=0.997,thr=0.950>, Top: 1< 1 >[Fa= 130 ]( 1 , 1 , 130 ),<|><>Tot Used: 301 , Added: 1 , Zero Std: 0 , Max Cor: 0.957
#>
15 <R=0.957,thr=0.950>, Top: 1< 1 >[Fa= 131 ]( 1 , 1 , 130 ),<|><>Tot Used: 301 , Added: 1 , Zero Std: 0 , Max Cor: 0.930
#>
16 <R=0.930,thr=0.900>, Top: 1< 1 >[Fa= 131 ]( 1 , 1 , 131 ),<|><>Tot Used: 301 , Added: 1 , Zero Std: 0 , Max Cor: 0.937
#>
17 <R=0.937,thr=0.900>, Top: 1< 1 >[Fa= 132 ]( 1 , 1 , 131 ),<|><>Tot Used: 301 , Added: 1 , Zero Std: 0 , Max Cor: 0.899
#>
18 <R=0.899,thr=0.800>, Top: 65< 4 >[Fa= 157 ]( 60 , 88 , 132 ),<|><>Tot Used: 323 , Added: 88 , Zero Std: 0 , Max Cor: 0.983
#>
19 <R=0.983,thr=0.950>, Top: 1< 1 >[Fa= 157 ]( 1 , 1 , 157 ),<|><>Tot Used: 323 , Added: 1 , Zero Std: 0 , Max Cor: 0.938
#>
20 <R=0.938,thr=0.900>, Top: 6< 1 >[Fa= 158 ]( 6 , 6 , 157 ),<|><>Tot Used: 323 , Added: 6 , Zero Std: 0 , Max Cor: 0.899
#>
21 <R=0.899,thr=0.800>, Top: 22< 2 >[Fa= 164 ]( 18 , 21 , 158 ),<|><>Tot Used: 328 , Added: 21 , Zero Std: 0 , Max Cor: 0.976
#>
22 <R=0.976,thr=0.950>, Top: 2< 1 >[Fa= 165 ]( 2 , 2 , 164 ),<|><>Tot Used: 328 , Added: 2 , Zero Std: 0 , Max Cor: 0.881
#>
23 <R=0.881,thr=0.800>, Top: 4< 1 >[Fa= 167 ]( 4 , 4 , 165 ),<|><>Tot Used: 329 , Added: 4 , Zero Std: 0 , Max Cor: 0.799
#>
24 <R=0.799,thr=0.800>
#>
[ 24 ], 0.9949082 Decor Dimension: 329 Nused: 329 . Cor to Base: 228 , ABase: 363 , Outcome Base: 0
#>
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]
pander::pander(sum(apply(dataframe[,varlist],2,var)))2.43e+21
pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))2.6e+14
pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))0.0195
pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))0.0632
varratio <- attr(DEdataframe,"VarRatio")
pander::pander(tail(varratio))| La_ECG_p_VFL_baseline | La_IT_CCV_LF | La_IT_BRV_prctile25 | La_IT_BRV_min | La_IT_BRV_max | La_IT_BRV_prctile75 |
|---|---|---|---|---|---|
| 9.21e-14 | 1.05e-24 | 3.86e-27 | 4.73e-31 | 2.5e-31 | 5.81e-32 |
1.5.1 The decorrelation matrix
if (!largeSet)
{
par(cex=0.6,cex.main=0.85,cex.axis=0.7)
UPLTM <- attr(DEdataframe,"UPLTM")
gplots::heatmap.2(1.0*(abs(UPLTM)>0),
trace = "none",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Decorrelation matrix",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Beta|>0",
xlab="Output Feature", ylab="Input Feature")
par(op)
}
1.5.2 Formulas Network
Displaying the features associations
par(op)
#if ((ncol(dataframe) < 1000) && (ncol(dataframe) > 10))
#{
# DEdataframeB <- ILAA(dataframe,verbose=TRUE,thr=thro,bootstrap=30)
transform <- attr(DEdataframe,"UPLTM") != 0
tnames <- colnames(transform)
colnames(transform) <- str_remove_all(colnames(transform),"La_")
transform <- abs(transform*cor(dataframe[,rownames(transform)])) # The weights are proportional to the observed correlation
VertexSize <- attr(DEdataframe,"fscore") # The size depends on the variable independence relevance (fscore)
names(VertexSize) <- str_remove_all(names(VertexSize),"La_")
VertexSize <- 10*(VertexSize-min(VertexSize))/(max(VertexSize)-min(VertexSize)) # Normalization
VertexSize <- VertexSize[rownames(transform)]
rsum <- apply(1*(transform !=0),1,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
csum <- apply(1*(transform !=0),2,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
ntop <- min(10,length(rsum))
topfeatures <- unique(c(names(rsum[order(-rsum)])[1:ntop],names(csum[order(-csum)])[1:ntop]))
rtrans <- transform[topfeatures,]
csum <- (apply(1*(rtrans !=0),2,sum) > 1)
rtrans <- rtrans[,csum]
topfeatures <- unique(c(topfeatures,colnames(rtrans)))
print(ncol(transform))
#> [1] 329
transform <- transform[topfeatures,topfeatures]
print(ncol(transform))
#> [1] 68
if (ncol(transform)>100)
{
csum <- (apply(1*(transform !=0),2,sum) > 1) & (apply(1*(transform !=0),1,sum) > 1)
transform <- transform[csum,csum]
print(ncol(transform))
}
if (ncol(transform) < 150)
{
gplots::heatmap.2(transform,
trace = "none",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Red Decorrelation matrix",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Beta|>0",
xlab="Output Feature", ylab="Input Feature")
par(op)
VertexSize <- VertexSize[colnames(transform)]
gr <- graph_from_adjacency_matrix(transform,mode = "directed",diag = FALSE,weighted=TRUE)
gr$layout <- layout_with_fr
fc <- cluster_optimal(gr)
plot(fc, gr,
edge.width = 2*E(gr)$weight,
vertex.size=VertexSize,
edge.arrow.size=0.5,
edge.arrow.width=0.5,
vertex.label.cex=(0.15+0.05*VertexSize),
vertex.label.dist=0.5 + 0.05*VertexSize,
main="Top Feature Association")
}
par(op)1.6 The heatmap of the decorrelated data
if (!largeSet)
{
hm <- heatMaps(data=DEdataframe[1:numsub,],
Outcome=outcome,
Scale=TRUE,
hCluster = "row",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
xlab="Feature",
ylab="Sample")
par(op)
}
1.7 The correlation matrix after decorrelation
if (!largeSet)
{
cormat <- cor(DEdataframe[,varlistc],method="pearson")
cormat[is.na(cormat)] <- 0
gplots::heatmap.2(abs(cormat),
trace = "none",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "Correlation after ILAA",
cexRow = cexheat,
cexCol = cexheat,
srtCol=45,
srtRow=45,
key.title=NA,
key.xlab="|Pearson Correlation|",
xlab="Feature", ylab="Feature")
par(op)
diag(cormat) <- 0
print(max(abs(cormat)))
}
[1]
1
1.8 U-MAP Visualization of features
1.8.1 The UMAP on Raw Data
classes <- unique(dataframe[1:numsub,outcome])
raincolors <- rainbow(length(classes))
names(raincolors) <- classes
topvars <- univariate_BinEnsemble(dataframe,outcome)
lso <- LASSO_MIN(formula(paste(outcome,"~.")),dataframe,family="binomial")
topvars <- unique(c(names(topvars),lso$selectedfeatures))
pander::pander(head(topvars))IT_MF_baseline, ECG_hrv_prctile25, ECG_hrv_mean, _ECG_hrv_geomean_A__, ECG_hrv_prctile75 and EDA_processed_mean_D
# names(topvars)
#if (nrow(dataframe) < 1000)
#{
datasetframe.umap = umap(scale(dataframe[1:numsub,topvars]),n_components=2)
# datasetframe.umap = umap(dataframe[1:numsub,varlist],n_components=2)
plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
text(datasetframe.umap$layout,labels=dataframe[1:numsub,outcome],col=raincolors[dataframe[1:numsub,outcome]+1])
#}1.8.2 The decorralted UMAP
varlistcV <- names(varratio[varratio >= 0.025])
topvars <- univariate_BinEnsemble(DEdataframe[,varlistcV],outcome)
lso <- LASSO_MIN(formula(paste(outcome,"~.")),DEdataframe,family="binomial")
topvars <- unique(c(names(topvars),lso$selectedfeatures))
pander::pander(head(topvars))La_ECG_RR_window_baseline, La_IT_BRV_baseline, La_EDA_processed_mad_D, La_EDA_Original_baseline_D, IT_p_Total_baseline and La_EDA_processed_trimmean25_D
varlistcV <- varlistcV[varlistcV != outcome]
# DEdataframe[,outcome] <- as.numeric(DEdataframe[,outcome])
#if (nrow(dataframe) < 1000)
#{
datasetframe.umap = umap(scale(DEdataframe[1:numsub,topvars]),n_components=2)
# datasetframe.umap = umap(DEdataframe[1:numsub,varlistcV],n_components=2)
plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After ILAA",t='n')
text(datasetframe.umap$layout,labels=DEdataframe[1:numsub,outcome],col=raincolors[DEdataframe[1:numsub,outcome]+1])
#}1.9 Univariate Analysis
1.9.1 Univariate
univarRAW <- uniRankVar(varlist,
paste(outcome,"~1"),
outcome,
dataframe,
rankingTest="AUC")100 : ECG_p_LF_mean 200 : IT_CCV_LF 300 : EDA_Original_mad_D
univarDe <- uniRankVar(varlistc,
paste(outcome,"~1"),
outcome,
DEdataframe,
rankingTest="AUC",
)100 : La_ECG_p_LF_mean 200 : La_IT_CCV_LF 300 : La_EDA_Original_mad_D
1.9.2 Final Table
univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")
##top variables
topvar <- c(1:length(varlist)) <= TopVariables
tableRaw <- univarRAW$orderframe[topvar,univariate_columns]
pander::pander(tableRaw)| caseMean | caseStd | controlMean | controlStd | controlKSP | ROCAUC | |
|---|---|---|---|---|---|---|
| ECG_hrv_prctile75 | -2.719 | 8.9741 | -5.8408 | 10.9387 | 0.00378 | 0.731 |
| ECG_hrv_geomean_A_ | 10.370 | 8.0477 | 13.8743 | 7.8682 | 0.00822 | 0.727 |
| IT_LF_baseline_D | 43.569 | 25.1600 | 26.4345 | 15.3449 | 0.61672 | 0.721 |
| IT_p_Total_baseline | 51.974 | 29.4230 | 31.5389 | 17.9800 | 0.71076 | 0.721 |
| IT_VLF_baseline | 57.578 | 32.3488 | 34.9418 | 19.7865 | 0.75500 | 0.720 |
| ECG_hrv_prctile25 | -12.471 | 7.7963 | -16.6349 | 6.7770 | 0.20654 | 0.719 |
| IT_PSD_baseline | 0.059 | 0.0376 | 0.0358 | 0.0228 | 0.21000 | 0.715 |
| ECG_hrv_mean | -7.294 | 5.4920 | -11.0369 | 6.0390 | 0.33833 | 0.714 |
| IT_HF_baseline | 3.308 | 3.5341 | 2.0033 | 2.1158 | 0.00564 | 0.713 |
| ECG_hrv_trimmean25 | -7.619 | 6.1613 | -11.3761 | 6.3193 | 0.35724 | 0.711 |
topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]
pander::pander(finalTable)| caseMean | caseStd | controlMean | controlStd | controlKSP | ROCAUC | |
|---|---|---|---|---|---|---|
| La_ECG_RR_window_baseline | 20.516 | 15.679 | 9.022 | 13.793 | 0.11840 | 0.784 |
| La_EDA_Original_mad_D | -7.578 | 10.562 | 1.170 | 9.564 | 0.01215 | 0.776 |
| La_EDA_processed_mad_D | 17.446 | 19.540 | 0.556 | 14.531 | 0.08373 | 0.766 |
| La_IT_BRV_baseline | -3.930 | 2.265 | -2.114 | 1.544 | 0.80056 | 0.756 |
| La_ECG_hrv_mean | -1.592 | 0.433 | -1.960 | 0.586 | 0.41819 | 0.741 |
| La_EDA_Original_baseline_D | -589.265 | 1714.012 | 639.035 | 1149.458 | 0.01696 | 0.739 |
| La_EDA_processed_std_D | 18.628 | 35.322 | -12.898 | 34.532 | 0.00649 | 0.730 |
| La_ECG_HR_min_div_baseline | 7.076 | 5.360 | 9.575 | 5.454 | 0.14465 | 0.727 |
| La_EDA_processed_trimmean25_D | 0.999 | 2.270 | -0.379 | 1.094 | 0.15207 | 0.721 |
| IT_p_Total_baseline | 51.974 | 29.423 | 31.539 | 17.980 | 0.71076 | 0.721 |
dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")
pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))| mean | total | fraction |
|---|---|---|
| 3.23 | 296 | 0.811 |
theCharformulas <- attr(dc,"LatentCharFormulas")
finalTable <- rbind(finalTable,tableRaw[topvar[!(topvar %in% topLAvar)],univariate_columns])
orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- theCharformulas[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]
Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores")
finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])| DecorFormula | caseMean | caseStd | controlMean | controlStd | controlKSP | ROCAUC | RAWAUC | fscores | |
|---|---|---|---|---|---|---|---|---|---|
| La_ECG_RR_window_baseline | - (0.875)ECG_RR_window_prctile75 + ECG_RR_window_baseline | 20.516 | 1.57e+01 | 9.0216 | 1.38e+01 | 0.11840 | 0.784 | 0.522 | 0 |
| La_EDA_Original_mad_D | - (0.831)EDA_Original_std_D + EDA_Original_mad_D | -7.578 | 1.06e+01 | 1.1699 | 9.56e+00 | 0.01215 | 0.776 | 0.507 | 0 |
| La_EDA_processed_mad_D | - (0.139)EDA_Original_std_D + EDA_processed_mad_D | 17.446 | 1.95e+01 | 0.5558 | 1.45e+01 | 0.08373 | 0.766 | 0.604 | -1 |
| La_IT_BRV_baseline | - (0.588)IT_BRV_mean + IT_BRV_baseline | -3.930 | 2.27e+00 | -2.1142 | 1.54e+00 | 0.80056 | 0.756 | 0.642 | -1 |
| La_ECG_hrv_mean | - (0.694)ECG_HR_min_div_mean + (0.681)ECG_HR_min_div_trimmean25 + ECG_hrv_mean - (0.916)ECG_hrv_trimmean25 | -1.592 | 4.33e-01 | -1.9604 | 5.86e-01 | 0.41819 | 0.741 | 0.714 | -1 |
| La_EDA_Original_baseline_D | + EDA_Original_baseline_D - (0.877)EDA_Filt1_prctile75_D | -589.265 | 1.71e+03 | 639.0354 | 1.15e+03 | 0.01696 | 0.739 | 0.504 | 0 |
| ECG_hrv_prctile75 | NA | -2.719 | 8.97e+00 | -5.8408 | 1.09e+01 | 0.00378 | 0.731 | 0.731 | NA |
| La_EDA_processed_std_D | - (0.295)EDA_Original_std_D + EDA_processed_std_D | 18.628 | 3.53e+01 | -12.8982 | 3.45e+01 | 0.00649 | 0.730 | 0.581 | 1 |
| La_ECG_HR_min_div_baseline | - (0.888)ECG_HR_min_div_mean + ECG_HR_min_div_baseline | 7.076 | 5.36e+00 | 9.5745 | 5.45e+00 | 0.14465 | 0.727 | 0.518 | -1 |
| ECG_hrv_geomean_A_ | NA | 10.370 | 8.05e+00 | 13.8743 | 7.87e+00 | 0.00822 | 0.727 | 0.727 | NA |
| La_EDA_processed_trimmean25_D | + EDA_processed_trimmean25_D - (0.652)EDA_processed_median_D | 0.999 | 2.27e+00 | -0.3787 | 1.09e+00 | 0.15207 | 0.721 | 0.582 | 0 |
| IT_LF_baseline_D | NA | 43.569 | 2.52e+01 | 26.4345 | 1.53e+01 | 0.61672 | 0.721 | 0.721 | NA |
| IT_p_Total_baseline | NA | 51.974 | 2.94e+01 | 31.5389 | 1.80e+01 | 0.71076 | 0.721 | 0.721 | 4 |
| IT_p_Total_baseline1 | NA | 51.974 | 2.94e+01 | 31.5389 | 1.80e+01 | 0.71076 | 0.721 | NA | NA |
| IT_VLF_baseline | NA | 57.578 | 3.23e+01 | 34.9418 | 1.98e+01 | 0.75500 | 0.720 | 0.720 | NA |
| ECG_hrv_prctile25 | NA | -12.471 | 7.80e+00 | -16.6349 | 6.78e+00 | 0.20654 | 0.719 | 0.719 | NA |
| IT_PSD_baseline | NA | 0.059 | 3.76e-02 | 0.0358 | 2.28e-02 | 0.21000 | 0.715 | 0.715 | NA |
| ECG_hrv_mean | NA | -7.294 | 5.49e+00 | -11.0369 | 6.04e+00 | 0.33833 | 0.714 | 0.714 | NA |
| IT_HF_baseline | NA | 3.308 | 3.53e+00 | 2.0033 | 2.12e+00 | 0.00564 | 0.713 | 0.713 | 0 |
| ECG_hrv_trimmean25 | NA | -7.619 | 6.16e+00 | -11.3761 | 6.32e+00 | 0.35724 | 0.711 | 0.711 | 4 |
1.10 Comparing ILAA vs PCA vs EFA
1.10.1 PCA
featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,scale. = TRUE) #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous])
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)
#pander::pander(pc$rotation)
PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])
gplots::heatmap.2(abs(PCACor),
trace = "none",
# scale = "row",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "PCA Correlation",
cexRow = 0.5,
cexCol = 0.5,
srtCol=45,
srtRow= -45,
key.title=NA,
key.xlab="Pearson Correlation",
xlab="Feature", ylab="Feature")
1.10.2 EFA
EFAdataframe <- dataframeScaled
if (length(iscontinous) < 2000)
{
topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)/2)
if (topred < 2) topred <- 2
uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE) # EFA analysis
predEFA <- predict(uls,dataframeScaled[,iscontinous])
EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous])
EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
gplots::heatmap.2(abs(EFACor),
trace = "none",
# scale = "row",
mar = c(5,5),
col=rev(heat.colors(5)),
main = "EFA Correlation",
cexRow = 0.5,
cexCol = 0.5,
srtCol=45,
srtRow= -45,
key.title=NA,
key.xlab="Pearson Correlation",
xlab="Feature", ylab="Feature")
}
1.11 Effect on CAR modeling
par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(rawmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
}
pander::pander(table(dataframe[,outcome],pr))| 0 | 1 | |
|---|---|---|
| 0 | 38 | 2 |
| 1 | 7 | 33 |
pander::pander(ptab$detail[c(5,3,4,6),])| statistic | est | lower | upper | |
|---|---|---|---|---|
| 5 | diag.ac | 0.887 | 0.797 | 0.947 |
| 3 | se | 0.825 | 0.672 | 0.927 |
| 4 | sp | 0.950 | 0.831 | 0.994 |
| 6 | diag.or | 89.571 | 17.389 | 461.391 |
par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe[,c(outcome,varlistcV)],control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(IDeAmodel,main="ILAA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(IDeAmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
}
pander::pander(table(DEdataframe[,outcome],pr))| 0 | 1 | |
|---|---|---|
| 0 | 36 | 4 |
| 1 | 8 | 32 |
pander::pander(ptab$detail[c(5,3,4,6),])| statistic | est | lower | upper | |
|---|---|---|---|---|
| 5 | diag.ac | 0.85 | 0.753 | 0.920 |
| 3 | se | 0.80 | 0.644 | 0.909 |
| 4 | sp | 0.90 | 0.763 | 0.972 |
| 6 | diag.or | 36.00 | 9.897 | 130.943 |
par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(PCAmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}
pander::pander(table(PCAdataframe[,outcome],pr))| 0 | 1 | |
|---|---|---|
| 0 | 23 | 17 |
| 1 | 0 | 40 |
pander::pander(ptab$detail[c(5,3,4,6),])| statistic | est | lower | upper | |
|---|---|---|---|---|
| 5 | diag.ac | 0.787 | 0.682 | 0.871 |
| 3 | se | 1.000 | 0.912 | 1.000 |
| 4 | sp | 0.575 | 0.409 | 0.730 |
| 6 | diag.or | Inf | NA | Inf |
par(op)1.11.1 EFA
EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(EFAmodel,EFAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
text(EFAmodel, use.n = TRUE,cex=0.75)
ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
}
pander::pander(table(EFAdataframe[,outcome],pr))| 0 | 1 | |
|---|---|---|
| 0 | 34 | 6 |
| 1 | 9 | 31 |
pander::pander(ptab$detail[c(5,3,4,6),])| statistic | est | lower | upper | |
|---|---|---|---|---|
| 5 | diag.ac | 0.812 | 0.710 | 0.891 |
| 3 | se | 0.775 | 0.615 | 0.892 |
| 4 | sp | 0.850 | 0.702 | 0.943 |
| 6 | diag.or | 19.519 | 6.230 | 61.147 |
par(op)